Magnetic resonance imaging (MRI) provides highly detailed anatomical information. Dynamic contrast-enhanced (DCE) MRI of the liver monitors the arrival, transit, or presence of contrast materials (e.g., gadolinium (Gd) chelates) through the liver. DCE MRI of other portions of the body (e.g., kidney, lung) may also monitor the arrival, transit, or presence of contrast materials. Conventionally, acquiring DCE abdominal images has been challenging due, for example, to motion artifacts caused by patient movement during multiple breath holds. It may be difficult to accommodate requests for multiple lengthy breath holds while a patient with a potentially compromised organ is in the bore while a contrast agent is being applied.
Acquiring useful images of the liver has been challenging due to the combination of a large volume to be covered, desired high spatial resolution, and rapidly changing contrast conditions in the post-contrast images. All of these factors are complicated by the need for multiple lengthy breath holds by a patient with a possibly compromised liver. Typical post contrast sequences may have required 15-20 second breath holds carefully coordinated with contrast agent administration, arrival, and uptake, which effectively precluded time-course analysis and which frequently resulted in motion-corrupted exams upon breath-hold failure.
Different contrast agents have been employed in liver MRI. For example, Gd-DTPA was used as early as 1988. More recently, Gd-BOPTA (gadolinium benzyloxy-propionic tetraacetate or gadobenate dimeglumine) and Gd-EOB-DTPA (gadolinium ethozybenzyl diethylenetriamine-pentaacetic acid) have been used. Gadolinium based contrast agents are typically employed to shorten T1 in regions where the Gd concentrates. Gd-BOPTA is distributed in the body like ordinary extracellular contrast agents (e.g., Gd-DTPA). However, in the liver, Gd-BOPTA is taken up by hepatocytes and is excreted into the biliary canaliculi in an adenosine triphosphate (ATP) dependent process. Hepatocytes are polarized cells that have two functionally distinct sides, including one that faces the blood and extracellular fluids. Gd-BOPTA enhancement may reach a peak 60-120 minutes after contrast agent introduction. Gd-EOB-DTPA combines hepatocellular specificity with T1-relaxivity and extracellular behavior. Gd-EOB-DTPA is first distributed into the extracellular spaces and then taken up by hepatocytes. Gd-EOB-DTPA enhancement may reach a peak in the liver about 20 minutes after contrast agent introduction.
Conventional approaches have typically employed T1-weighted, gradient recalled echo (GRE) sequences. T1 refers to spin-lattice relaxation, T2 refers to spin-spin relaxation. T1 relaxation is caused by interactions between excited protons and local electromagnetic fields associated with neighboring structures. T2 relaxation depends on the continuous de-phasing of precessing protons caused by local magnetic field inhomogeneities. T2 is faster than T1. A GRE sequence applies varying gradient fields to refocus spins. A spin echo (SE) sequence uses RF pulses to refocus spins. An echo planar imaging (EPI) sequence may be used to acquire all the spatial-encoding data of an image after a single radio-frequency (RF) excitation. Instead of measuring just one echo after an excitation pulse. EPI acquires many echoes. Echoes may be acquired as long as the precessing magnetization in the xy plane has not decayed beyond an acquisition threshold. EPI may be thought of as an “add-on” to a pulse sequence that facilitates acquiring more signals from each excitation pulse. When an EPI acquisition strategy is used, all k-space lines may be measured in one TR of a gradient echo sequence or a spin echo sequence.
Three-dimensional (3D) acquisitions may have provided continuous whole-liver coverage to assess whole-liver perfusion, but have been limited by longer acquisition times. 3D T1 mapping within one breath-hold has typically been challenging given the size of the liver. Thus, two-dimensional (2D) images have typically been acquired with higher temporal and spatial resolution. However, the 2D image approach may have been limited to a single representative slice or selected slices, which precluded whole liver perfusion analysis. Achieving higher temporal and spatial resolution facilitates achieving greater precision in estimating liver perfusion rates.
In 2012, a rotating 2D multi-echo approach was described in Lee et al., Proc. ISMRM 2012, p. 3012. This approach produced relatively equidistant samples regardless of time scale. This approach was applied in time-resolved four dimensional (4D) contrast-enhanced MR angiography. See, for example, Rapid Time-Resolved Magnetic Resonance Angiography via a Multiecho Radial Trajectory and GraDes Reconstruction, Lee et al., MRM 2012 (doi: 10.1002/mrm.24256). This approach may be referred to herein as the Lee approach. In the angiography application, performing reconstruction at a long time scale (e.g., around 2 minutes) allowed sensitivity maps and field maps to be computed. Performing reconstruction at a shorter time scale (e.g., around 1-2 seconds) allowed dynamic imaging of the vasculature.
The 3D multi-echo non-Cartesian echo planar imaging (EPI) Lee approach employs pseudo-random rotations of a single 2D multi-echo non-Cartesian readout in a multi-shot trajectory. The trajectory produces incoherent aliasing artifacts and a relatively uniform distribution of projections over different time scales. A field map is computed from the same data set and is used to avoid signal dropout in regions of substantial field inhomogeneity. A compressed sensing reconstruction using a gradient descent with sparsification (GraDeS) algorithm may be employed. The GraDeS algorithm as adapted for use with multi-coil MRI data is given by:
            x      ^        n    =                    x        ^                    n        -        1              +                  1        y            ⁢                        ∑                      i            =            1                                n            e                          ⁢                                  ⁢                              C            i            *                    ⁢                      F            *                    ⁢                      D            ⁡                          (                                                y                  i                                -                                                      FC                    i                                    ⁢                                                            x                      ^                                                              n                      -                      1                                                                                  )                                          
where {circumflex over (x)}n is the image estimate after iteration number n, C*i are the complex conjugate coil sensitivities, and F* is the adjoint NUFFT operation (non-Cartesian k space to image space). The summation corresponds to a multi-coil gridding reconstruction of the difference between the acquired k space data, y, and k space values corresponding to the current image estimate. The new estimate is made by moving a step size 1/γ along this gradient. The procedure progressively reduces the error ∥y−Ax∥2.
In the GraDeS algorithm, using a larger number of iterations improves temporal behavior at the cost of decreased image signal-to-noise ratio (SNR). The GraDeS algorithm assumes that at a point in time, the difference between a current frame and a previous frame should be minimal. However, in objects that experience significant movement due, for example, to respiration, the frames may differ by an unacceptable amount. Conventionally this may have limited the Lee approach to imaging static objects.
In the Lee angiography approach, when using a multichannel receiver array for data acquisition, the resulting k space data is made up of nc sets corresponding to each of the individual coils. yi is the k space data corresponding to coil i. and x corresponds to the object to be reconstructed. The relationship between image space and k space is given by:
  y  =                    A        x            ⁢                          ⁢      where      ⁢                          ⁢      y        =                            [                                                                      y                  1                                                                                    ⋮                                                                                      y                                      n                    e                                                                                ]                ⁢                                  ⁢        A            =              [                                                            FC                1                                                                        ⋮                                                                          FC                                  n                  e                                                                    ]            
The matrix A is a system matrix representing the linear transformation of an image to multi-coil k space data. Ci are diagonal matrices containing the complex coil sensitivities, and F is a matrix representing a linear transformation from image space to k space. In the non-Cartesian (e.g., radial) case, F may represent a Fourier transform followed by interpolation from a Cartesian k space grid to the non-Cartesian k space locations, which may be referred to as a non-uniform fast Fourier transform (NUFFT). A gridding reconstruction for multi-coil data is described by:{circumflex over (x)}grid=Σi=1neC*iF*Dyi 
where D is a diagonal matrix containing the density compensation weights for each k space sample. Density compensation accounts for the non-uniform sampling density present in the radial k space sampling pattern. C*i are the complex conjugate coil sensitivities, and F* is the adjoint NUFFT operation.
The Lee angiography method involves sampling a number of radial lines within a single plane using a 2D radial echo-planar imaging (EPI) trajectory. Multiple rotations of the same 2D trajectory are used to fill in 3D k space. A pseudo-random schedule of rotations is employed to produce incoherent aliasing artifacts at any arbitrarily chosen number of shots per reconstructed image frame. The full set of shots may be used to determine coil sensitivity maps. The individual echoes of the multi-echo radial trajectory are used to determine a field map.
In one example of the Lee approach, images were acquired using a non-Cartesian 3D FLASH acquisition (TR=8.68 ms, flip angle=20, 1-mm isotropic resolution), with a 3T scanner. A minimum-phase radiofrequency pulse (duration 600 μs, tip-down time 140 μs from end) was used for slab-selective excitation. A 2D radial EPI trajectory having five projections per shot (duration=6.44 ms) was acquired in each TR interval starting at echo time=0.26 ms. The additional echo time (TE) times within the readout for the full echoes were 1.63, 2.89, 4.15, and 5.42 ms. Data were acquired continuously throughout the trajectory duration. A 2.6-μs sampling interval (2476 total samples) was used, corresponding to 2-fold oversampling along each readout line. Pseudo-random rotations of the 2D pattern were used to progressively fill in 3D k space over multiple shots.
Thus, the Lee angiography approach involved acquiring data using a 3D multi-echo non-Cartesian (e.g., radial) approach by using pseudo-random rotations of a single 2D multi-echo non-Cartesian readout, and then reconstructing the acquired data using a compressed sensing reconstruction with GraDeS. The approach may have been susceptible to motion artifacts in a moving object.